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# Fraction Operations

## Objective

Multiply a whole number by a mixed number.

## Common Core Standards

### Core Standards

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• 4.NF.B.4.B — Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)

## Criteria for Success

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1. Multiply a mixed number by a whole number using a visual model, repeated addition, the distributive property, or converting the mixed number to a fraction greater than 1 (i.e., an "improper" fraction) and using the general method, i.e., ${{n \times {a\over b} }= { {n\times a} \over b}}$

## Tips for Teachers

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#### Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Task 1 (benefits from discussion) and Anchor Task 2 (can be done independently). Find more guidance on adapting our math curriculum for remote learning here.

#### Fishtank Plus

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• Problem Set
• Student Handout Editor
• Google Classrom Integration
• Vocabulary Package

## Anchor Tasks

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### Problem 1

1. Draw a diagram to represent each of the following. Then find the product.

a.   ${2\times4}$

b.   ${2\times{1\over3}}$

c.   ${2\times4}{1\over3}$

1. What do you notice about #1? What do you wonder?

#### Guiding Questions

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### Problem 2

Estimate the following products. Then solve.

a.   ${3\times5{1\over4}}$

b.   ${4\times6{3\over5}}$

c.   ${5\times9{7\over10}}$

#### Guiding Questions

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### Problem 3

Juliette decided to solve part (a) of Anchor Task #2 by doing the following:

${3\times2{1\over4} =3\times\left(2+{1\over4}\right)=3\times{9\over4}}$

Do you agree with Juliette’s strategy? Will it yield the same product?

Which strategy is more efficient, Juliette’s or the distributive property? What about for the other problems in Anchor Task #2?

#### Guiding Questions

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## Problem Set & Homework

#### Discussion of Problem Set

• What were the two ways you solved #3? Which one was more efficient?
• How would you correct Nick’s work in #4?
• Which expressions were equivalent in #5? Which were not? How do you know?
• What did the student do incorrectly in #7? What is the correct product?
• Did anyone attempt #8? What did you get?

## Target Task

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Solve. Show or explain your work.

1.   ${4 \times 5{3\over8}}$

2.   ${3\times 4{3\over10}}$

### Mastery Response

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## Additional Practice

#### Unit Practice

With Fishtank Plus you can access our Daily Word Problem Practice and our content-aligned Fluency Activities created to help students strengthen their application and fluency skills.

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